An analysis of variables influencing a combustion process in a combustion chamber is known from S. M. Candel, Combustion Instability Coupled by Pressure Waves and their Active Control.
In this analysis, linear methods, such as a regression analysis, are used in order to investigate dependences between the influencing variables and their influence on the combustion process.
However, as a combustion process taking place in a combustion chamber is a complex process observing non-linear dependences of influencing factors, such ‘linear’ analysis methods, such as from Candel, offer unreliable and insufficiently accurate results with regard to the influence of variables on the combustion process.
A further analysis of a combustion process is known from J. Hermann, et al., Aktive Instabilitätskontrolle an einer 170 MW Gasturbine, in this case a combustion process in a combustion chamber of a gas turbine, a so-called annular combustion chamber-gas turbine V84.3A.
Moreover, an occurrence of oscillations and/or pressure fluctuations during a combustion process in a combustion chamber of a gas turbine is known from J. Hermann, et al, in this case the annular combustion chamber-gas turbine V84.3A and damage to the combustion chamber caused by the resulting vibrations.
It is described in J. Hermann, et al that these oscillations and/or vibrations, so-called humming and/or combustion chamber humming, arise due to regenerative feedback from combustion processes taking place simultaneously in the combustion chamber of the gas turbine.
The vibrations cause an unstable flame front, which in turn causes increased heating of the combustion chamber. These can lead to damage to the combustion chamber of the gas turbine.
In order to be able to take suitable remedial action against the problem of combustion oscillations, in J. Hermann, et al the oscillation phenomenon is investigated in detail and possibilities for its removal, in particular active and passive methods, are compared and discussed.
J. Hermann, et al establishes and/or proposes to eliminate the damaging oscillations by constructive optimization of a combustion chamber geometry.
To counter possible repeatedly occurring oscillation problems where the operating capacity of the gas turbine is increased, J. Hermann, et al proposes an active instability control (AIC) based on an anticyclical modulation of a fuel flow.
However, AIC requires costly sensor and actuator technology which restricts its possibility of use.
It is further known that this damaging humming can also be reduced or avoided by reducing a load on the gas turbine, i.e. it is known that the load on a gas turbine has a great influence on combustion chamber humming and/or a high dependence or correlation with the (damaging) combustion chamber humming.
The reduction of the load to reduce or avoid damage to a combustion chamber of a gas turbine is, however, a possible solution which is only conditionally practicable.
As a rule, performance pledges are given by power station operators to their customers which, with a reduction in performance of the gas turbines, run the risk of not being fulfilled.
Consequently, it is important to be aware of further variables influencing the combustion process and/or the humming in addition to those of the load, the geometry and the fuel flow, for the reduction or prevention of damaging combustion chamber humming.
Generally, it is therefore desirable to ascertain with sufficient accuracy the influence of individual variables influencing the combustion process, in addition to dependences of variables influencing one another qualitatively and/or quantitatively.
This knowledge could, in particular, allow the general approach to the problem in the field of combustion processes to be solved and to be able to reduce more efficiently or more cost effectively the problem of combustion chamber humming especially by other influencing variables and/or suitable combinations of other variables.
Data Analysis by Using a Network
It is generally known to use networks made up of nodes and links in an area of data analysis, in order to identify and to describe complex data structures and dependences of data in the data structures.
Such a data analysis is known from DE 10159262.0 by using a network of the ‘causal network’ type.
Seen graphically, such a causal network is a statistical model of the data described thereby.
Such a causal network, such as from DE 10159262.0, is moreover particularly suitable for identifying and describing statistical properties of data, for example statistical dependence and/or independence between two variables.
Furthermore, from DE 10159262.0 a method for removing identifiable links from a network is known, a so-called Polynomial-Complexity-Method (PC method).
A data analysis by using a causal network, which is of the Bayesian and/or Bayes network W. Jensen, F. V. (1996), An introduction to Bayesian networks sub-type, is also known from DE 10159262.0.
In this data analysis by means of the Bayesian network, statistical dependences and/or statistical independences, generally statistical properties, between the data are determined (learned). The statistical properties of the data can then be graphically represented by using the network of nodes and links (FIG. 3).
FIG. 3 shows this graphical representation with the network 300 of nodes 310 and links 320. Two respective nodes 310 of the network 300 are connected to one another by a link 320.
A node 310 of the network 300 represents a datum (variable). A link 320 represents a statistical dependence between the nodes 310 and/or variables connected by this link 320. Unconnected nodes 310 are statistically independent of one another.
FIG. 4 shows diagrammatically a procedure 400 during a data analysis according to the PC method known from DE 10159262.0 which leads, for example, to the network structure 300 shown in FIG. 3.
The object of the data analysis is the determination of dependences and/or independences between data to be analyzed and a representation of the dependences and/or independences between the data, thus of a structure contained in the data, by means of a network structure and/or by means of a network.
A ‘structure contained in the data’ is generally understood to be a statistical dependence and/or a statistical independence between the variables.
The data for the data analysis are the variables v, w, x, y and z. Data tuples (v, w, x, y, z)i are given, where i=1 . . . N (N=number of the predetermined data tuples).
During the analysis, a statistical dependence and/or independence between the variables v, w, x, y and z is determined.
FIG. 5 shows a network 500 made up of nodes A 510, B 511, C 512, D 513 and E 514 which represent the variables v, w, x, y and z.
In a first step 410 of the method 400 by using a statistical test method, a χ2-Test, which is described in χ2-Test, a statistical independence and/or statistical dependence is determined between two respective variables, for example (v,x), (x,z) or (v, y) (zero order statistical independence and/or dependence).
In a second step 420, from the network 500 which has an initial configuration where all nodes are connected to one another with links, such links 521 which connect two respective nodes, for example (A,E), (C,D) and (C, E), for whose associated variables a statistical independence was determined, for example (v,z), (x, y) and (x, z) are removed.
In a third step 430 for two respective variables, for which a statistical dependence has been determined, a conditional statistical dependence and/or independence is determined conditional on a third variable, for example (v, x|w), (v, y|w) or (w, x|v) (1st order statistical independence and/or dependence). In addition, the χ2-Test, which is described in χ2-Test is used.
In a fourth step 440 such links 522 in the network 500, which respectively connect two nodes, for example (A, C), (B, D) and (D, E) for whose associated variables a conditional statistical independence was determined, are removed.
According to the fourth step the network 500 has a structure (end configuration) which describes the statistical properties of the data.
Bayesian Network
A causal network, a Bayesian (Bayes) network is known from Jensen.
A Bayesian network B is a special form of representation of a common multivariate probability density function (pdf) of a number of variables X by means of a graphical model.
It is defined by a directed acyclic graph, (DAG) G, wherein each node i=1, . . . , n corresponds to a random variable Xi.
The edges between the nodes represent statistical dependences and can be interpreted as causal relations between them. The second part of the Bayesian network is the number of conditional pdfs P(Xi|Pai, θ, G), which are parameterized by a vector θ.
These conditional pdfs specify the type of dependences for the individual variables i from the number of their parents Pai. The common pdf can therefore be broken down into the product form
                              P          ⁡                      (                                          X                1                            ,                                                X                  2                                ⁢                                         ,                              …                ⁢                                                                  ⁢                                  X                  n                                ⁢                                                )                          =                    ⁢                                    ∏                              i                =                1                            n                        ⁢                                                  ⁢                          P              ⁡                              (                                                                            X                      i                                        ❘                                          Pa                      i                                                        ,                  θ                  ,                  G                                )                                                                        (        1        )            
The DAG of a Bayesian network describes in an unequivocal way the conditional dependence- and independence relationships between a set of variables, although conversely a given statistical structure of the pdf does not result in an unequivocal DAG.
Instead it can be shown that two DAGs describe the same pdf, when and only when they have the same set of edges and the same set of ‘colliders’, whereby a collider is a constellation wherein at least two directed edges converge in the same node.
From DE 19611732 a further method is known for determining weights of a neural network suitable for removal and for removing weights from a neural network, a so-called pruning method.